Question and Answers Forum

All Questions      Topic List

Differential Equation Questions

Previous in All Question      Next in All Question      

Previous in Differential Equation      Next in Differential Equation      

Question Number 104240 by bemath last updated on 20/Jul/20

$$\frac{dy}{dx}=1+x^2+y^2+{\left(xy\right)}^2$$

Commented by bemath last updated on 20/Jul/20

$$thankyouall.correct$$

Answered by OlafThorendsen last updated on 20/Jul/20

$$\frac{dy}{dx}=(1+x^2)(1+y^2)$$$$\frac{dy}{1+y^2}=(1+x^2)dx$$$$\arctan y=\mathrm{C}+x+\frac{x^3}{3}$$$$y=\tan (\mathrm{C}+x+\frac{x^3}{3})$$$$$$

Answered by 1549442205PVT last updated on 20/Jul/20

$$\frac{\mathrm{dy}}{\mathrm{dx}}=1+{\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{x}}^2{\mathrm{y}}^2=(1+{\mathrm{x}}^2)(1+{\mathrm{y}}^2)$$$$\iff \frac{\mathrm{dy}}{1+{\mathrm{y}}^2}=(1+{\mathrm{x}}^2)\mathrm{dx}.\mathrm{Integrate}\mathrm{two}$$$$\mathrm{sides}\mathrm{we}\mathrm{get}$$$$\arctan \mathrm{y}=\mathrm{x}+\frac{{\mathrm{x}}^3}{3}+{\mathrm{C}}_1$$$$\Rightarrow \mathrm{y}=\tan (\mathrm{x}+\frac{{\mathrm{x}}^3}{3})+\mathrm{C}$$$$\mathrm{Is}\mathrm{it}\mathrm{correct},\mathrm{Sir}?.\mathrm{Please}\mathrm{check}\mathrm{to}\mathrm{help}$$$$\mathrm{me}.$$

Answered by Dwaipayan Shikari last updated on 20/Jul/20

$$\frac{\mathrm{dy}}{\mathrm{dx}}=(1+{\mathrm{x}}^2)(1+{\mathrm{y}}^2)$$$$\int \frac{\mathrm{dy}}{1+{\mathrm{y}}^2}=\int (1+{\mathrm{x}}^2)\mathrm{dx}$$$${\tan }^{-1}\mathrm{y}=(\mathrm{x}+\frac{{\mathrm{x}}^3}{3}+{\mathrm{C}}_1)$$$$\mathrm{y}=\tan (\mathrm{x}+\frac{{\mathrm{x}}^3}{3}+{\mathrm{C}}_1)$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com